Print or Internet but not both

I originally posted this problem in the General forum but was sent here. I am a long-time Mac user but don't understand networking very well and am shaky with Windows. I have read through the sticky about printing and searched the forum but can't seem to find a solution to my problem.

Here is my setup:

MacBook Pro Core 2 Duo 2.33 GHz 3GB, OS 10.4.8
DSL modem (ethernet)
HP LaserJet 4050N (ethernet)
Parallels Desktop Build 1970, Windows XP Pro SP2

With Bridged Ethernet, I can print fine, but can't access the Internet. With Shared Networking, I can access the Internet but can't print. In other words:

Bridged Ethernet = Printing but no Internet
Shared Networking = Internet but no printing

In case it matters, I used Bonjour to install the printer, using the generic driver; I also tried the HP 4050 driver.

I will be grateful for any help.

Thank you,

David

 

How is the printer accessed - network or USB? If USB, does OS X own it or does Windows own it?

 

The printer is connected to the Mac via ethernet. I think this means it is connected through a LAN?

David

 

In case it matters, I should have said that both the printer and DSL modem are connected each by an ethernet cord to an ethernet hub, which is connected to the Mac.

David